2.3.152 Problems 15101 to 15200

Table 2.877: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
15101	18232	\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.786
15102	18449	\begin{align*} x^{\prime }&=2 x+y-2 z+2-t \\ y^{\prime }&=1-x \\ z^{\prime }&=x+y-z+1-t \\ \end{align*}	✓	✓	✓	✓	1.786
15103	8255	\begin{align*} 2 y+y^{\prime }&=3 x -6 \\ \end{align*}	✓	✓	✓	✓	1.787
15104	17593	\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\sec \left (3 t \right ) \\ \end{align*}	✓	✓	✓	✓	1.787
15105	23175	\begin{align*} y^{\prime }-2 y x&=x^{2} \\ \end{align*}	✓	✓	✓	✓	1.787
15106	6117	\begin{align*} -a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.788
15107	18004	\begin{align*} y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\ \end{align*}	✓	✓	✓	✓	1.788
15108	26300	\begin{align*} \left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.788
15109	845	\begin{align*} y^{\prime \prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.789
15110	227	\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\ y \left (1\right ) &= 3 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.791
15111	10107	\begin{align*} y^{\prime \prime }-y x -x^{3}+2&=0 \\ \end{align*}	✓	✓	✓	✓	1.791
15112	11449	\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \\ \end{align*}	✓	✓	✓	✓	1.791
15113	15947	\begin{align*} y^{\prime }&=3 y+{\mathrm e}^{7 t} \\ \end{align*}	✓	✓	✓	✓	1.791
15114	18230	\begin{align*} y^{\prime \prime }-4 y^{\prime }&=2 \cos \left (4 x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.792
15115	20402	\begin{align*} y&={y^{\prime }}^{2} x +y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.792
15116	11683	\begin{align*} {y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \\ \end{align*}	✓	✓	✓	✗	1.793
15117	14759	\begin{align*} x y^{\prime \prime }-y^{\prime } \left (x^{2}+2\right )+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.793
15118	15958	\begin{align*} y^{\prime }+5 y&=3 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✓	1.793
15119	25464	\begin{align*} y^{\prime }&=a \left (t \right ) y+\delta \left (-t +s \right ) \\ \end{align*}	✓	✓	✓	✓	1.793
15120	10179	\begin{align*} \left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.794
15121	27597	\begin{align*} {y^{\prime \prime }}^{4}&={y^{\prime }}^{5}-y {y^{\prime }}^{3} y^{\prime \prime } \\ \end{align*}	✓	✓	✗	✗	1.794
15122	16485	\begin{align*} y^{\prime \prime }+5 y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	1.796
15123	14132	\begin{align*} y^{\prime \prime \prime }-y&=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2} \\ \end{align*}	✓	✓	✓	✓	1.797
15124	27489	\begin{align*} 3 x^{2}-y&=\sqrt {x^{2}+1}\, y^{\prime } \\ \end{align*}	✓	✓	✓	✓	1.797
15125	216	\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}	✓	✓	✓	✓	1.798
15126	8039	\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=0 \\ \end{align*}	✓	✓	✓	✓	1.798
15127	3574	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.799
15128	7007	\begin{align*} y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\ \end{align*}	✓	✓	✓	✓	1.799
15129	8420	\begin{align*} y^{\prime }&=5 y \\ \end{align*}	✓	✓	✓	✓	1.799
15130	9867	\begin{align*} 2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.799
15131	17134	\begin{align*} y^{\prime }&=y^{2}-y \\ \end{align*}	✓	✓	✓	✓	1.799
15132	21003	\begin{align*} x^{\prime }+\ln \left (3\right ) x&=0 \\ \end{align*}	✓	✓	✓	✓	1.799
15133	23399	\begin{align*} 3 x y^{\prime \prime }-4 y^{\prime }+\frac {5 y}{x}&=0 \\ \end{align*}	✓	✓	✓	✗	1.799
15134	25415	\begin{align*} y+y^{\prime }&=7 \operatorname {Heaviside}\left (-4+t \right ) \\ \end{align*}	✓	✓	✓	✓	1.799
15135	8765	\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=2 x \,{\mathrm e}^{x}-1 \\ \end{align*}	✓	✓	✓	✗	1.801
15136	9872	\begin{align*} 2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.801
15137	17132	\begin{align*} y^{\prime }&=3 y \\ \end{align*}	✓	✓	✓	✓	1.801
15138	661	\begin{align*} y^{\prime }&=-y-\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	1.803
15139	22542	\begin{align*} y^{\prime \prime }&=y^{\prime }+2 x \\ \end{align*}	✓	✓	✓	✓	1.803
15140	149	\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.804
15141	2581	\begin{align*} t^{2} y^{\prime \prime }-t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.804
15142	13704	\begin{align*} y^{\prime \prime }+\left (a \,x^{3} b +b \,x^{2}+2 a \right ) y^{\prime }+a^{2} \left (b \,x^{3}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.804
15143	15582	\begin{align*} y^{\prime }&=1-y \\ y \left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	1.804
15144	16405	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.804
15145	15074	\begin{align*} x^{\prime \prime }-4 x^{\prime }+4 x&={\mathrm e}^{t}+{\mathrm e}^{2 t}+1 \\ \end{align*}	✓	✓	✓	✓	1.805
15146	27347	\begin{align*} y^{\prime }&=2+\left (y-2 x \right )^{{1}/{3}} \\ \end{align*}	✓	✓	✓	✓	1.805
15147	1294	\begin{align*} t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.806
15148	13948	\begin{align*} y^{\prime \prime }+\left (2 a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.806
15149	22306	\begin{align*} x^{\prime \prime }&=t^{2}-4 t +8 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}	✓	✓	✓	✓	1.806
15150	25584	\begin{align*} y^{\prime \prime }+y^{\prime }&=4 \\ \end{align*}	✓	✓	✓	✓	1.806
15151	27298	\begin{align*} x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\ x \left (0\right ) &= b \\ \end{align*}	✓	✓	✓	✓	1.806
15152	1836	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=2 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}	✓	✓	✓	✗	1.807
15153	13289	\begin{align*} y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b \,{\mathrm e}^{s x} \\ \end{align*}	✓	✓	✓	✗	1.807
15154	15526	\begin{align*} y^{\prime }&=1-y \\ \end{align*}	✓	✓	✓	✓	1.807
15155	17666	\begin{align*} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	1.807
15156	27748	\begin{align*} y^{\prime \prime }+\left (x^{4}+1\right ) y&=0 \\ \end{align*}	✗	✓	✓	✗	1.807
15157	6392	\begin{align*} {y^{\prime }}^{2}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	1.808
15158	14389	\begin{align*} x^{\prime }&=3 y-3 x \\ y^{\prime }&=x+2 y-1 \\ \end{align*}	✓	✓	✓	✓	1.808
15159	194	\begin{align*} y^{\prime }&=x^{2}-2 y x +y^{2} \\ \end{align*}	✓	✓	✓	✓	1.809
15160	2542	\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	1.809
15161	5722	\begin{align*} y^{\prime \prime }+y&=\sin \left (a x \right ) \sin \left (b x \right ) \\ \end{align*}	✓	✓	✓	✗	1.809
15162	9176	\begin{align*} \ln \left (y\right ) y-2 y x +\left (x +y\right ) y^{\prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.810
15163	13685	\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y&=0 \\ \end{align*}	✓	✓	✓	✗	1.810
15164	14720	\begin{align*} x^{2} y^{\prime \prime }-2 y&=4 x -8 \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	1.810
15165	15788	\begin{align*} y^{\prime }&=\frac {4 t}{1+3 y^{2}} \\ \end{align*}	✓	✓	✓	✗	1.810
15166	20403	\begin{align*} {y^{\prime }}^{2} x +a x&=2 y y^{\prime } \\ \end{align*}	✓	✓	✗	✓	1.811
15167	23370	\begin{align*} 3 x^{2} y^{\prime \prime }+4 x y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.811
15168	8053	\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-\cos \left (y\right ) y^{\prime }+y y^{\prime } \sin \left (y\right )\right ) \\ \end{align*}	✓	✓	✓	✗	1.812
15169	18438	\begin{align*} x^{\prime }&=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }&=\tan \left (t \right )-x \\ \end{align*}	✓	✓	✓	✓	1.812
15170	2580	\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.813
15171	5724	\begin{align*} y^{\prime \prime }+y&=x \left (\cos \left (x \right )-x \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	1.813
15172	6080	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-6 x y^{\prime }-4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.813
15173	16492	\begin{align*} 4 y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.813
15174	18337	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=\frac {1}{x^{2}+1} \\ y \left (\infty \right ) &= \frac {\pi ^{2}}{8} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✗	✓	1.813
15175	18205	\begin{align*} y^{\prime \prime }+a^{2} y&=2 \cos \left (m x \right )+3 \sin \left (m x \right ) \\ \end{align*}	✓	✓	✓	✓	1.814
15176	9869	\begin{align*} x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.816
15177	15169	\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=\cos \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.816
15178	16957	\begin{align*} {y^{\prime }}^{2}+y&=0 \\ \end{align*}	✓	✓	✓	✓	1.816
15179	12974	\begin{align*} \left (b +a y\right ) y^{\prime \prime }+c {y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	1.817
15180	9920	\begin{align*} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.818
15181	25527	\begin{align*} m y^{\prime \prime }+k y&=f \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	1.818
15182	17853	\begin{align*} y^{\prime }&=-x +y \\ \end{align*}	✓	✓	✓	✓	1.819
15183	23468	\begin{align*} x y^{\prime \prime }-2 y^{\prime }+\frac {\left (x^{2}+2\right ) y}{x}&=4+\tan \left (x \right ) \\ \end{align*}	✓	✓	✓	✗	1.819
15184	7697	\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	1.820
15185	17990	\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \\ \end{align*}	✓	✓	✓	✓	1.821
15186	13895	\begin{align*} \left (a \,x^{2}+b x +c \right )^{2} y^{\prime \prime }+A y&=0 \\ \end{align*}	✓	✓	✓	✗	1.822
15187	16958	\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	1.822
15188	21600	\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\ \end{align*}	✓	✓	✓	✗	1.822
15189	22856	\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.822
15190	6230	\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.823
15191	7605	\begin{align*} 6 w^{\prime }-13 w&=0 \\ \end{align*}	✓	✓	✓	✓	1.823
15192	15110	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	1.823
15193	1500	\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	1.824
15194	27473	\begin{align*} y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \\ \end{align*}	✓	✓	✓	✗	1.825
15195	6096	\begin{align*} 2 y+3 y^{\prime }+x \left (1-x \right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	1.826
15196	12838	\begin{align*} y^{\prime \prime }-6 y^{2}+4 y&=0 \\ \end{align*}	✓	✓	✓	✗	1.826
15197	22867	\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.826
15198	27264	\begin{align*} x \left (y^{\prime }-y\right )&={\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	1.826
15199	9944	\begin{align*} 2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	1.827
15200	15659	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*}	✓	✓	✓	✓	1.827